The discussion in Section REF  has established that the time complexity of NEURAL is \(\mathcal {O}(\vert V_{C} \vert + \vert E_{C} \vert )\) . To show this empirically, we use the LFR Benchmark [1]} for generating synthetic networks with \(\mu =0.4\) . Louvain algorithm is used for community detection, and the largest community is considered as the target community such that \(\vert E_{C} \vert \)  lies within the range \(10^{3} - 10^{8}\) . The results are averaged over 10 such synthetic networks. We record the run times for two deception strategies (based on greedy optimization): (i) SADDEN and (ii) NEURAL (we fix \(\beta \)  as default i.e., \(\beta =0.3|V_{C}|\) ). Fig. REF  shows that the run time for NEURAL increases linearly with \(\vert E_{C} \vert \)  thereby verifying the analytical time complexity shown in Section REF  (\(\vert E_{C} \vert >> \vert V_{C} \vert \) ; \(\mathcal {O}(\vert V_{C} \vert + \vert E_{C} \vert )\)  \(\approx \)  \(\mathcal {O}(\vert E_{C} \vert )\) ). We also observe that with an increase in \(\vert E_{C} \vert \) , NEURAL outperforms SADDEN in terms of its run time.
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